Traditional wireless communication systems are half-duplex; that is, they are not capable of transmitting and receiving signals simultaneously on a single wireless communications channel. Recent work in the wireless communications field has led to advancements in developing full-duplex wireless communications systems; these systems, if implemented successfully, could provide enormous benefit to the wireless communications field. For example, the use of full-duplex communications by cellular networks could cut spectrum needs in half. One major roadblock to successful implementation of full-duplex communications is the problem of self-interference. While progress has been made in this area, solutions intended to address self-interference have failed to successfully address non-linearities resulting from the conversion of a baseband digital signal to a transmitted RF signal (during transmission) and the conversion of a received RF signal back to a baseband digital signal (during reception). Thus, there is a need in the wireless communications field to create new and useful systems and methods for non-linear digital self-interference cancellation. This invention provides such new and useful systems and methods.